Details

sample36.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	164	17
4	339	17
5	596	17
6	819	17
7	926	17
8	1192	17
9	1633	17
10	1697	17
11	1698	17
done	1698	17

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.7b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
5.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series350.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
43.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
92.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
182.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify978.0ms

Counts

71 → 71

Iterations

Useful iterations: done (974.0ms)

Iter	Nodes	Cost
0	129	985
1	246	962
2	572	857
3	1554	852
done	5000	849

prune342.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
14.0b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.0b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
8×	`pow1` `div-exp` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 125

Calls

4 calls:

65.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
3.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series269.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
61.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
57.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
99.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.9s

Counts

137 → 137

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	213	3145
1	545	2834
2	1540	2163
3	4256	2146
done	5000	1983

prune444.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

21.0ms	(* (+ z 6.012459259764103) z)
48.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
85.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
70.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series316.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (+ z 6.012459259764103) z)
69.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
56.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
142.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.4s

Counts

108 → 108

Iterations

Useful iterations: 2 (348.0ms)

Iter	Nodes	Cost
0	198	1630
1	547	1386
2	2014	1209
done	5001	1209

prune396.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.1b	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.6b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
15.0ms	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
5.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series303.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
43.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
138.0ms	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
96.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify1.8s

Counts

95 → 95

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	142	1731
1	304	1690
2	831	1494
3	2787	1481
done	5001	1478

prune361.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes235.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.4b

bsearch145.0ms

Steps

Iters	Range		Point
8	0.5242272119756929	639.503948019383	629.303371294859
7	-533721278393.32306	-2445851338.3862987	-2642213428.445614

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	25	44
1	31	36
done	31	36

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8000×

body

valid